Last season you might recall a dust-up between Harvard evolutionary psychologist Steven Pinker and popular science author Malcolm Gladwell over whether teams really have any ability to predict which college QBs will pan out into good pros. You might be wondering what the heck a psychologist and a pop-science author have to do with NFL football.

In his book What the Dog Saw, Gladwell wrote about how hard it is for school administrators to discriminate the better teacher candidates from the lesser candidates. Gladwell used the NFL draft to illustrate how difficult it is for anyone to predict human performance, even in a sport where there is ample performance metrics and every step, throw, and catch is videotaped from 12 different angles. Gladwell was referring to what was reported by economists Dave Berri and Rob Simmons as a "very weak" correlation between draft order and per-play performance by QBs.

In an exchange of letters following Pinker's critical review of What the Dog Saw, Pinker took issue with Gladwell's claim that there was "no connection" between when a QB is taken in the draft and his per-play performance. Pinker wrote that this is "simply not the case."

As has been pointed previously, the problem with the weak correlation cited by Gladwell is that it excludes players who are not judged good enough by coaches during their development to warrant much if any playing time. At its core, the NFL draft is a process of selection, and we should expect selection bias will taint most attempts at analysis. Gladwell looked at the draft process and (correctly) said:

"Coaches and GMs turn out to be good decision-makers when it comes to drafting quarterbacks when you consider the fact that the quarterbacks who never played aren’t any good. And how do we know that the quarterbacks who never play aren’t any good? Because coaches and GMs are good decision-makers!”

But Gladwell's argument cuts both ways. The only way to see that coaches and GMs aren't any good at drafting QBs is to assume they're no good at choosing which QB on their roster to play in games!

In this post I'll attempt to settle the question of whether NFL scouts really have any ability to identify the better QBs. Do the QBs picked higher in the draft turn out to be better performers on a per-play basis? Is Pinker correct that they do, or is Gladwell correct that they do not?

Over his career, Roethlisberger has averaged 6.7 net yards per attempt (NYPA) and a 3.4% interception rate. In 2009, the league average was 6.2 NYPA and 3.1% int rate. According to my game probability model, all things being equal, Roethlisberger's passing stats would turn an average team into one with a 57% chance of beating an average opponent.

If we replace him with a substitute for a few games, it's hard to predict how the Steelers' passing game would do. But just as an exercise, say their passing game drops by one standard deviation. Their NYPA would be 5.7 and their int rate would be 4.5%. All else equal, this would drop them from a 57% team to a 40% team.

When I started to get really interested in sports statistics I thought, "Somebody should write a Freakonomics, but about sports." I was woefully uninformed about the vast library of research already done, particularly about baseball. At first I (foolishly) thought, "Maybe I could write that book." I did some clicking around and I was crushed to learn there already was one.

At my first opportunity I ran out and bought Wages of Wins. I thought," This is cool. I could do this too." So I'll always carry a debt of gratitude for authors Dave Berri, Martin Schmidt, and Stacey Brook. I didn't agree with everything in Wages, but it asked all the right questions and got me thinking about sports in a whole new way. Besides, if you're waiting for the sports book that you'll agree with 100%, you'll be waiting a long time.

Is quarterback performance related to where a passer is taken in the draft? It may seem like a silly question, but the answer is more complicated (and controversial) than it first seems. What if I said that the correlation between a QB’s draft rank and his career adjusted Yards Per Attempt (AdjYPA) is only -0.07? You’d think that’s amazingly small. (The correlation coefficient would be -1 if the relationship between draft order and performance is perfectly proportional, and it would be 0 if there is no relationship at all.)

What if I told you the correlation coefficient is -0.72? That’s more like it, you’d think. But which correlation coefficient is correct? They both are.

Adam Archuleta became one of the most sought-after NFL free agents in 2006. Several teams were interested in the playmaking strong safety, but the Redskins won the bidding, making him the highest paid safety in history at the time. Owner Dan Snyder signed-off on giving Archuleta a 6-year $30 million contract, with $10 million guaranteed.

To call the Archuleta signing a bust would be an understatement. He started only 7 games the next season and was traded to Chicago for a 6th-round draft pick the following year. Archuleta never returned to his early-career form, and washed out of the league after the 2007 season.

Although Snyder has a well-known, and well-deserved, reputation for overpaying for disappointing free agents, he's not alone. There's a phenomenon of auctions that makes overpaying for top free agent players all too common.

I've given in and created a Twitter account. You may have noticed it over there on the sidebar. The goal is not to keep readers up to date on what I had for breakfast (eggs with sausage, onions, and diced habanero peppers topped with Sriracha sauce--my favorite by the way). The primary goal is to share interesting links in a timely way or make comments that aren't worthy of a full post. I also like it because the 140-character limit forces me to be tight and pithy with my thoughts. It's a good exercise for the brain.

Economists Richard Thaler and Cade Massey authored a widely-read research paper analyzing the value of NFL draft picks, and they've recently published an updated version. The paper's primary finding was that teams are overconfident in their ability to choose the best players. In essence, the very top picks are overvalued relative to later picks, both in terms of what teams are willing to trade to move up in the draft and in terms of salary.

Recently Richard Thaler penned an article for the NYT discussing his paper. But puzzlingly, he goes on to make a claim that clearly contradicts his own research. He writes, "it makes absolutely no sense to be giving so much money to unproven rookies, many of whom turn out to be busts." Further, he writes, "veteran players would probably agree with the principle that eight-figure salaries should be reserved for players who have already proved themselves on the field."

The model's approach is very similar to my football model. Basketball is a much simpler sport, though. There's no field position, down, or distance in basketball. Score and time remaining are really the only significant factors.

Back in 1997 I was spent Easter Sunday with a good friend. His brother, who lived in the La Jolla area of San Diego, hosted us for dinner. On the drive up the La Jolla ridge overlooking the Pacific, my friend pointed over to the right side of the road and said, "That's Junior Seau's house." I caught a glimpse of number 55, along with what looked like a dozen family members filing out of a couple vans in front of the house. They were the largest human beings I had ever seen. The women were large, the men were unimaginably large, and even the children seemed enormous. Junior somehow appeared to be the runt of the family. I got the impression Samoans were all giants.

Last season there were 30 NFL players of Somoan descent, and 200 more playing Division IA college football. (Here's a list from 2008.) That's a lot of players from a group of people whose entire population could easily fit into an NFL stadium. Earlier this year 60 Minutes aired a profile on Samoan football, and if you missed it it's a great story. (I've embedded the clip at the end of this article. Edit--CBS has killed the link.)

Undoubtedly, the culture and character of the Samoan people are factors in their disproportionate level of success in football. But, as my drive through La Jolla suggested, hereditary traits may also play a role. Still, how can a single small island produce so many top players?

Raheem Morris, whose leadership added 20.401 points to his team’s performance, was actually the best coach of the 2009 season. The worst was Brad Childress, who cost his team 10.401 points over the course of the regular season. Bill Belichick was actually slightly below average. How can we say this? I’ve developed a method of determining the contribution of a coach to his team. The exciting thing is that, as you’ll see at the end of this article, this method can be applied to any sport, not just football.

It’s actually pretty simple, as you’ll see below. There’s a just little calculus involved, plus some matrix math, and a healthy dose of Laplace transforms. Basically, the only new principle involved is that instead of predictive power being generated by the relative measure of yards (and points), it is produced by the medial interaction of stochastic-reluctance and correlative directance. It all starts with the assumption that competitive coaching performance, of any type, is distributed according to a Gaussian distribution.

@BBurkeESPN

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